The nonlinearity of the Z2-Kerdock code Km+1, where m is an odd integer ≥3, is not at all obvious. By regarding Km+1 as the binary image of the Z4-Kerdock code .,K(m) under the Gray map[1], a simple proof can be achi...
IT is known that the average undetected error probability (UEP) of a binary [n, k] code Con a binary symmetric channel with crossover probability p is given byPe(p) = sum from i=1 Aipi
1 Preliminaries The mathematical definition of the two-dimensional optical orthogonal code(2-D OOC)is as follows: Definition 1. A(mn, ω,λ_a,λ_c) 2-DOOC consists of a set of(O, 1) m×n matri-
NGUYEN et al. give a method for constructing binary CP constant-weight (CPC) codes,then they construct protocol sequences with good performance by using the codes. To makethe minimum distance of the CP codes large eno...
In Ref.[2] the author dealt with the Main conjecture on geometric codes andproved the correctness of the conjecture for codes arising from curves with genus 1 or2 when the cardinal of the ground field is large enough....
Ⅰ. INTRODUCTION AND MAIN RESULTS Hermitian codes, which are the particular case of cyclotomic Goppa codes are investigated in [2] and [3], but the results on the minimum distance are incomplete. A Hermitian curve ove...
Self-dual linear codes are a sort of important code. For self-dual geometric Goppa codes, Driencourt and Stichtenoth showed a criterion, which is too complex to use well. In this note, we give a simple criterion for e...
For the hyperelliptic curve y^2=f(x) over F_q with deg(f)≥5, there is a singular point (0, 1, 0), such that a curve is not smooth. But the codes which are constructed by using hyperelliptic curves can be discussed ba...
<正> Let X be an alphabet. The measure on the language family monoid 2~x which consist,of all languages over X is introduced by [1] as follows. Let π be a probability distribution on X, and be homomorphically extende...
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Let the alphabet X = {a, b}. We discuss the language B = {a^iba^j|i, j≥ 0} over X. Clearly, the word of B can be represented by the point (i, j) in the plane, or by